The concepts of (λ ,μ)−fuzzy subsemigroup and various (λ ,μ)−fuzzy ideals of a semigroup were introduced by generalizing (∈,∈∨q)−fuzzy subsemigroup and (∈,∈∨q)−fuzzy ideal. The regular semigroup was characterized by the properties of the middle parts of various (λ ,μ)−fuzzy ideals, and several equivalence conditions of regular semigroups were obtained.

In this paper, it is shown that the value semigroup of a prime divisor of the second kind on a 2-dimensional regular local ring is symmetric. Further, a necessary and sufficient condition for two prime divisors of the second kind on a 2-dimensional regular local ring to have the same value semigroup is obtained.

The main theme of this paper is to study ordered semihypergroups in the context of int-soft interior hyperideals. In this paper, the notion of int-soft interior hyperideals are studied and their related properties are discussed. We present characterizations of interior hyperideals in terms of int-soft interior hyperideals. The concepts of int-soft hyperideals and int-soft interior hyperideals c...

For a linearly ordered set X we consider the relative rank of the semigroup of all order preserving mappingsOX on X modulo the full transformation semigroup TX . In other words, we ask what is the smallest cardinality of a set A of mappings such that 〈OX ∪A 〉 = TX . When X is countably infinite or well-ordered (of arbitrary cardinality) we show that this number is one, while when X = R (the set...

Rauzy graphs of subshifts are endowed with an automaton structure. For Sturmian subshifts, it is shown that its transition semigroup is the syntactic semigroup of the language recognized by the automaton. A projective limit of the partial semigroups of nonzero regular elements of their transition semigroups is described. If the subshift is minimal, then this projective limit is isomorphic, as a...

The Temperley-Lieb and Brauer algebras and their cyclotomic analogues, as well as the partition algebra, are all examples of twisted semigroup algebras. We prove a general theorem about the cellularity of twisted semigroup algebras of regular semigroups. This theorem, which generalises a recent result of East about semigroup algebras of inverse semigroups, allows us to easily reproduce the cell...